In the figure, PA is tangent to semicircle SAR, PB is tangent to semicircle RBT, and SRT is a straight line. If arc AS is 63 degrees and arc BT is 42 degrees, then find angle APB, in degrees.
Let midpoints of SR and RT be M and N
MAP and NBP are right angles
∠AMS = 63º ∠BNT = 42º
AMNBP is a pentagon (sum of interior angles of a pentagon is 540º)
∠APB = 540 - (180 + 117 +138) = 105º